Transcript Bayesian integration of external information into the single step approach for genomically enhanced prediction of breeding values J.

Bayesian integration of external
information into the single step
approach for genomically enhanced
prediction of breeding values
J. Vandenplas, I. Misztal, P. Faux, N.
Gengler
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Introduction
• Unbiased EBV if genomic, pedigree and
phenotypic information considered simultaneously
• Problem
– Only records related to selected animals available
– Bias due to genomic pre-selection
• Single step genomic evaluation (ssGBLUP)
– Simultaneous combination of genomic, pedigree and
phenotypic information (=internal information)
– No integration of external information (e.g. MACE-EBV)
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Objective
• Integration of a priori known external information
into ssGBLUP
– By a Bayesian approach
– To avoid multi-step methods
– By considering
• simplifications of computational burden,
• a correct propagation of external information,
• and no multiple considerations of contributions due to
relationships.
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Methods
• Bayesian approach (Dempfle, 1977; Legarra et al., 2007)
• 2 groups of animals
1) animals I = internal animals with only records in
 Ia: non genotyped animals
Ib: genotyped animals
2) animals E = external animals with records in
possible records in
 Ea: non genotyped animals
Eb: genotyped animals
and
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Methods
•
An internal evaluation
–
–
–
All animals Ia, Ib, Ea, Eb
Only
instead of
where
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Methods
•
An unknown external ssGBLUP
–
–
–
All animals Ia, Ib, E
Genomic information included in
Only
( precorrected for fixed effects)
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Methods
• Problem
– Unknown external ssGBLUP
• Available
– External genetic evaluation of animals Ea and Eb
• without animals Ia and Ib
• without genomic information

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Methods
• Substitution in the unknown external ssGBLUP
–
and
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Methods
•
Finally, internal evaluation = ssGBLUP
integrating external information
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Methods
•
Approximations and simplifications of
computational burden
 RHS: add a product between a matrix and a vector
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Methods
•
Approximations and simplifications of
computational burden
 LHS: add a block diagonal matrix
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Simulation
•
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